Gao Jian | Searcharxiv

arXiv2023

Empirical extinction coefficients for the Swift-UVOT optical-through-ultraviolet passbands

We calculated empirical reddening and extinction coefficients with respect to the dust reddening map of Schlegel et al. for the Swift-UVOT passbands, using the 'star pair' method and photometric data from the UVOT Serendipitous Source Catalogue and spectroscopic data from LAMOST Data Release 7 and 2MASS. The reddening coefficients for the UVW2-UVM2, UVM2-UVW1, UVW1-U, U-B, and B-V colors are -1.39, 2.08, 0.78, 0.72, and 0.84, respectively.The extinction coefficients for the UVW2, UVM2, UVW1, U, B, and V bands are 5.60, 6.99, 4.91, 4.13, 3.41 and 2.57, respectively. The numbers are consistent with predictions by the Fitzpatrick's extinction law of R(V)=3.0. Temperature-dependent variations of the coefficients are found and discussed, particularly for the ultraviolet passbands. We recommend using the new reddening and extinction coefficients in future when dereddening the Swift-UVOT data.

astro-ph.IM↗

arXiv2016

On a class of left metacyclic codes

Let $G_{(m,3,r)}=\langle x,y\mid x^m=1, y^3=1,yx=x^ry\rangle$ be a metacyclic group of order $3m$, where ${\rm gcd}(m,r)=1$, $1<r<m$ and $r^3\equiv 1$ (mod $m$). Then left ideals of the group algebra $\mathbb{F}_q[G_{(m,3,r)}]$ are called left metacyclic codes over $\mathbb{F}_q$ of length $3m$, and abbreviated as left $G_{(m,3,r)}$-codes. A system theory for left $G_{(m,3,r)}$-codes is developed for the case of ${\rm gcd}(m,q)=1$ and $r\equiv q^ε$ for some positive integer $ε$, only using finite field theory and basic theory of cyclic codes and skew cyclic codes. The fact that any left $G_{(m,3,r)}$-code is a direct sum of concatenated codes with inner codes ${\cal A}_i$ and outer codes $C_i$ is proved, where ${\cal A}_i$ is a minimal cyclic code over $\mathbb{F}_q$ of length $m$ and $C_i$ is a skew cyclic code of length $3$ over an extension field of $\mathbb{F}_q$. Then an explicit expression for each outer code in any concatenated code is provided. Moreover, the dual code of each left $G_{(m,3,r)}$-code is given and self-orthogonal left $G_{(m,3,r)}$-codes are determined.

cs.IT↗